Abstract
We start with the classical sampling theorem for bandlimited signals and comment on its various extensions. In Section 2 we discuss the problem of sampling harmonic functions. In the subsequent section we consider nonuniform sampling of bandlimited signals and entire functions of exponential type. We present a new sampling theorem which can be deduced from a recent result by one of us. As the main result of the whole paper, we show in Section 4 that there is an equivalence between sampling of signals and sampling of entire harmonic functions. This is applied to the theorem in Section 3. As a consequence, we get a new uniqueness theorem for entire harmonic functions of exponential type.
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Schmeisser, G., Voss, J.J. (1997). A New Interpretation of the Sampling Theorem and Its Extensions. In: Nürnberger, G., Schmidt, J.W., Walz, G. (eds) Multivariate Approximation and Splines. ISNM International Series of Numerical Mathematics, vol 125. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8871-4_22
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DOI: https://doi.org/10.1007/978-3-0348-8871-4_22
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9808-9
Online ISBN: 978-3-0348-8871-4
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